Abstract
In two experiments we evaluated the coactivation of arithmetic facts and the possible inhibitory mechanism used to select the correct one. To this end, we introduced an adapted version of the negative priming paradigm in which participants received additions and they decided whether they were correct or not. When the addition was incorrect but the result was that of multiplying the operands (e.g., 2 + 4 = 8), participants took more time to respond relative to control additions with unrelated results. This finding corroborated that participants coactivated arithmetic facts of multiplications even when they were irrelevant to perform the task. Moreover, the participants were slower to respond to an addition whose result was that of multiplying the operands of the previous trial (e.g., 2 + 6 = 8). These results support the existence of an inhibitory mechanism involved in the selection of arithmetic facts.
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Notes
The analysis of second trial depending on the type of first trial. It is important to note that the type of second trial (multiplication 2 vs. unrelated 2) could not be analyzed depending on the type of first trial (multiplication 1 vs. unrelated 1) due to a repetition effect that might have a different impact on the two conditions of trial 2. For example, while the solution 8 is repeated in the multiplication 2 condition: 2 + 6 = 8, after the multiplication 1 condition 2 + 4 = 8; the solution 10 is repeated in the unrelated 2 condition 4 + 6 = 10 after the unrelated 1 condition 2 + 4 = 10. Note, however, that this unbalanced repetition effect is avoided when multiplication 2 and unrelated 2 conditions are directly compared since in both conditions, half of the solutions were explicitly presented in the previous trial. Nevertheless, we performed additional analyses to evaluate the influence of Trial 1 on Trial 2 by avoiding the unbalanced repetition effect. Firstly, the Trial 1 (multiplication 1, unrelated 1 condition) x Trial 2 (multiplication 2, unrelated 2) interaction was significant, F(1,47) = 17.55, p < 0.05, η 2 = 0.27. Afterward, we compared the two conditions that involved repetition: (a) multiplication 1–multiplication 2 condition vs. (b) unrelated 1–unrelated 2 condition. The RTs in Trial 2 were 100 ms slower in (a) vs. (b), F(1,47) = 6.18, p < 0.05, η 2 = 0.12, suggesting that, in spite of the repetition effect, Trial 2 was difficult to perform when it included the result of multiplying the operands of Trial 1. However, the comparison between (c) multiplication 1–unrelated 2 vs. (d) unrelated 1 vs. related 2 was not significant, F(1,47) = 2.71, p > 0.05, η 2 = 0.05 (57 ms difference). These two conditions did not involve repeating the result. Hence, the consequences of inhibiting the result of multiplying the operands of Trial 1 were only evident in Trial 2 when the result was visually present in both trials, the (a) condition.
Possible differences due to the gender of participants were examined. In Experiment 1, the results obtained in the first trial did not show differences between females and males, F(1,46) = 1.61, p > 0.05, η 2 = 0.03, and the Gender × Type of addition result was not significant F < 1. In the second trial, Gender was not a significant variable, F(1,46) = 2.35, p > 0.05, η 2 = 0.05, nor this variable interacted with type of results of previous trial, F < 1. In Experiment 2, the results of trial 1 did not show a significant effect of Gender, F < 1, and this variable did not interact with type of addition results, F < 1. In the second trial, Gender was not significant, F(1,31) = 1.12, p > 0.05, η 2 = 0.03, and this variable did not interact with type of result of previous trial, F(1,31) = 1.20, p > 0.05, η 2 = 0.04. Hence, there were no differences due to the gender of participants in this study.
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Acknowledgments
This research was supported by the Spanish Ministry of Economy and Competitiveness (Grant PSI2012–32287) and by the Programa de Generación de Conocimiento Científico de Excelencia de la Fundación Séneca, Agencia de Ciencia y Tecnología de la Región de Murcia (research project 08741/PHCS/08). Patricia Megías is a Ph.D. candidate in Psychology (RD99/2011) at the University of Granada. We are greatly indebted to two anonymous reviewers for lots of useful theoretical and empirical comments. We thank Jamie I. D. Campbell for giving us permission upon request to use his database (Campbell & Xue, 2001) to corroborate that the additions used in the two conditions of trial 2 were equated in response latency and accuracy when individuals solve them without any manipulation.
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Megías, P., Macizo, P. & Herrera, A. Simple arithmetic: evidence of an inhibitory mechanism to select arithmetic facts. Psychological Research 79, 773–784 (2015). https://doi.org/10.1007/s00426-014-0603-3
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DOI: https://doi.org/10.1007/s00426-014-0603-3